Penguin b→sℓ′+ℓ′− and B-meson anomalies in a gauged Lμ − Lτ

The Z′-gauge boson in an U(1)Lμ−Lτ gauge symmetry has two interesting features: one is its vector couplings to the charged leptons, and the other is the decoupling from the electron. Based on these properties, we investigate the feasibility to simultaneously resolve the RK(⁎)=BR(B→K(⁎)μ+μ−)/BR(B→K(⁎)e+e−) and RD(⁎)=BR(B¯→D(⁎)τν¯τ)/BR(B¯→D(⁎)ℓν¯ℓ) anomalies in an U(1)Lμ−Lτ model, where the former is expected to arise from the Z′-penguin-induced b→sμ+μ− process and the latter from the tree-level b→cτν¯τ decay. In order to achieve the intended purpose, we employ one vector-like doublet lepton and one singlet scalar leptoquark (LQ), in which the new particles all carry the U(1)Lμ−Lτ charges; the b→sZ′ effective interaction is generated from the vector-like lepton and LQ loop, and the b→cτν¯τ decay is induced from the LQ. When the constraints from the b→sγ, B+→K+νν¯, Bc−→τν¯τ, ΔF=2, and τ→μℓℓ¯ processes are included, it is found that RD and RD⁎ can be enhanced to fit the experimental data, and the Wilson coefficient C9 from the LQ-loop can reach C9LQ,μ∼−1, which can explain the RK and RK⁎ anomalies. In addition, in this simple model, the Higgs lepton-flavor violating h→μτ decay can occur at the tree level, and its branching ratio can be as large as the current experimental upper limit.